Problem: The equation of a circle $C$ is $x^2+y^2-10x+6y+25 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Answer: To find the equation in standard form, complete the square. $(x^2-10x) + (y^2+6y) = -25$ $(x^2-10x+25) + (y^2+6y+9) = -25 + 25 + 9$ $(x-5)^{2} + (y+3)^{2} = 9 = 3^2$ Thus, $(h, k) = (5, -3)$ and $r = 3$.